Decomposing abundance change to recruitment and loss: analysis of the North-American avifauna

.title[
# Decomposing abundance change to recruitment and loss: analysis of the North-American avifauna
]
.author[
### François Leroy Marta Jarzyna Petr Keil 
]
.institute[
### Czech University of Life Sciences, Prague Ohio State University
]

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# Temporal change of abundance

* Sensitive indicator of biodiversity state

* Perturbed by human activities

* Average decline of relative abundance `$\rightarrow$` 69% (Living Planet Index)

]

]

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# Decomposing abundance change

**Abundance change:** 
`$$\Delta N = N_{t1} - N_{t0} = R - L$$`

`$$\Leftrightarrow \Delta^2N = \Delta R - \Delta L$$`

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# Decomposing growth rate

* **Growth rate:** per individual average change in population

`$$\frac{\Delta N}{N_{t0}} = \frac{R}{N_{t0}} - \frac{L}{N_{t0}}$$`

--

`$$\big\Downarrow$$`

* **Recruitment rate** = individual addition of individuals

`$$\frac{R}{N_{t0}}$$`

]

`$$\big\Downarrow$$`

* **Loss rate** = individual probability of dying/emigrating

`$$\frac{L}{N_{t0}}$$`

]

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## Problem

`$\Rightarrow$` Assessing the ongoing decrease of abundance does not tell us how loss and recruitment change through time

`$\Rightarrow$` Decrease in recruitment `$\neq$` Increase in loss, but they both result in an acceleration of the decrease of abundance

### From a conservation perspective

`$\rightarrow$` measures to "bend the curve" of recruitment (*e.g.* working on reproductive sucess, protecting breeding habitat)

`$$\neq$$`

`$\rightarrow$` measures to "bend the curve" of loss (*e.g.* reduction of threats, increasing habitat quality)

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## For North-American avifauna, we assessed:

###  1) temporal change of abundance, recruitment and loss from 1987 and 2021

### 2) temporal change of growth rate, recruitment rate and loss rate

### 3) which process (recruitment or loss) is driving temporal change of biodiversity

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# Data - Breeding Bird Survey (BBS)

* Structured data on North American avifauna

* From 1987 to 2021

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* More than 1000 routes

* 564 species

]

]

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# Model - Dail & Madsen

`$$N_{t+1} = Survival_{t+1} + Recruitment_{t+1}$$`
.center[

#### with

]

`$$Survival_{t+1} \sim Bin(N_t, \omega)$$`

`$$Recruitment_{t+1} \sim Poisson(\gamma)$$`

`$$Loss_t = N_t - S_{t+1}$$`
--

* Accounting for detection probabilities, depending on meteorological covariates:

`$$N^*{_t} \sim Bin(N_t, p)$$`

`$\Rightarrow$` **Sky condition, wind condition, temperature** & **time of the day**
]

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# Model - Dail & Madsen

* 3 MCMC chains per species `$\times$` 564 species `$=$` **1692 MCMC chains**

.center[
`$\Rightarrow$` **9.3 years** to fit the model using 1 core ( `$\sim$` 1 year using 8 cores)
]

<img src="data:image/png;base64,#images/jarzyna.1.jpg" width="30%" />
]
]

]

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# Trend in abundance

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# Trend in recruitment
 
.center[
<img src="data:image/png;base64,#images/map_rec.jpg" width="100%" />
]

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# Trend in loss
 
.center[
<img src="data:image/png;base64,#images/map_loss.jpg" width="100%" />
]

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# Trends in abundance, recruitment and loss
 
.center[
<img src="data:image/png;base64,#images/map_all_number.jpg" width="90%" />
]

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# Trend in growth rate

<img src="data:image/png;base64,#images/map_gr.png" width="100%" />
]

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# Trend in recruitment rate

<img src="data:image/png;base64,#images/map_recRate.png" width="90%" />
]

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# Trend in loss rate

<img src="data:image/png;base64,#images/map_lossRate.png" width="90%" />
]

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# Trends in growth, recruitment and loss rates

<img src="data:image/png;base64,#images/map_rates_all.png" width="90%" />
]

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# Recruitment vs. Loss rates

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# Recruitment vs. Loss rates

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# Recruitment vs. Loss rates

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# Recruitment vs. Loss rates

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# Recruitment vs. Loss rates

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# Recruitment vs. Loss rates

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# Recruitment vs. Loss rates

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# Recruitment vs. Loss rates

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# Recruitment vs. Loss rates

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# Recruitment vs. Loss rates

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# Recruitment rate vs. Loss rate

<img src="data:image/png;base64,#images/recRVsLossR.png" width="100%" />
]

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# Recruitment rate vs. Loss rate (smoothened)

<img src="data:image/png;base64,#images/map_recRVsLossR_gam.png" width="90%" />
]

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# Species' preferred habitat - Numbers

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# Species' preferred habitat - Rates

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# Conclusion

* At the **community level**: decrease in the number of extinction and recruitment drive biodiversity change

]

.pull-right[
* At the **individual level**: increase in recruitment and extinction rate are driving the population dynamic

]

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# Conclusion

`$\Rightarrow$` From a conservation perspective, working at the individual level is the most important

`$\Rightarrow$` Focus must be done on bending the loss rate curve (*e.g.* habitat loss, fragmentation, predation by domestic animals...)

]

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# Ackowledgements

.pull-left[
<svg viewBox="0 0 512 512" style="position:relative;display:inline-block;top:.1em;fill:white;height:1em;" xmlns="http://www.w3.org/2000/svg"> <path d="M464 64H48C21.49 64 0 85.49 0 112v288c0 26.51 21.49 48 48 48h416c26.51 0 48-21.49 48-48V112c0-26.51-21.49-48-48-48zm0 48v40.805c-22.422 18.259-58.168 46.651-134.587 106.49-16.841 13.247-50.201 45.072-73.413 44.701-23.208.375-56.579-31.459-73.413-44.701C106.18 199.465 70.425 171.067 48 152.805V112h416zM48 400V214.398c22.914 18.251 55.409 43.862 104.938 82.646 21.857 17.205 60.134 55.186 103.062 54.955 42.717.231 80.509-37.199 103.053-54.947 49.528-38.783 82.032-64.401 104.947-82.653V400H48z"></path></svg> leroy@fzp.czu.cz

<img src="data:image/png;base64,#images/jarzyna.1.jpg" width="30%" />
]

]

.pull-right[
<svg viewBox="0 0 512 512" style="position:relative;display:inline-block;top:.1em;fill:lightblue;height:2em;" xmlns="http://www.w3.org/2000/svg"> <path d="M459.37 151.716c.325 4.548.325 9.097.325 13.645 0 138.72-105.583 298.558-298.558 298.558-59.452 0-114.68-17.219-161.137-47.106 8.447.974 16.568 1.299 25.34 1.299 49.055 0 94.213-16.568 130.274-44.832-46.132-.975-84.792-31.188-98.112-72.772 6.498.974 12.995 1.624 19.818 1.624 9.421 0 18.843-1.3 27.614-3.573-48.081-9.747-84.143-51.98-84.143-102.985v-1.299c13.969 7.797 30.214 12.67 47.431 13.319-28.264-18.843-46.781-51.005-46.781-87.391 0-19.492 5.197-37.36 14.294-52.954 51.655 63.675 129.3 105.258 216.365 109.807-1.624-7.797-2.599-15.918-2.599-24.04 0-57.828 46.782-104.934 104.934-104.934 30.213 0 57.502 12.67 76.67 33.137 23.715-4.548 46.456-13.32 66.599-25.34-7.798 24.366-24.366 44.833-46.132 57.827 21.117-2.273 41.584-8.122 60.426-16.243-14.292 20.791-32.161 39.308-52.628 54.253z"></path></svg> @FrsLry

<img src="data:image/png;base64,#images/petr_keil.jpg" width="33%" />
]
]

]

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# Per species change - Abundance

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# Per species change - Recruitment

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# Per species change - Loss

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# Per species change - Growth rate

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# Per species change - Recruitment rate

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# Per species change - Loss rate

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# Rec. vs. Loss colored by ab. trend

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# Rec. rate vs. Loss rate colored by growth rate